To solve for [tex]\( x \)[/tex] in the equation
[tex]\[ \frac{1}{2} - x + \frac{3}{2} = x - 4, \][/tex]
follow these steps:
1. Simplify the left-hand side:
Combine the constants [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{2} \)[/tex]:
[tex]\[ \frac{1}{2} + \frac{3}{2} = \frac{4}{2} = 2. \][/tex]
So the equation simplifies to:
[tex]\[ 2 - x = x - 4. \][/tex]
2. Rearrange the equation to isolate [tex]\( x \)[/tex]:
Add [tex]\( x \)[/tex] to both sides of the equation to eliminate the [tex]\( -x \)[/tex] term on the left-hand side:
[tex]\[ 2 - x + x = x - 4 + x, \][/tex]
which simplifies to:
[tex]\[ 2 = 2x - 4. \][/tex]
3. Isolate the [tex]\( x \)[/tex] term:
Add 4 to both sides of the equation to move the constant term on the right-hand side to the left:
[tex]\[ 2 + 4 = 2x, \][/tex]
which simplifies to:
[tex]\[ 6 = 2x. \][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{6}{2} = 3. \][/tex]
Therefore, the solution for [tex]\( x \)[/tex] is [tex]\( 3 \)[/tex].
Given the choices, the correct answer is:
A. [tex]\( x = 3 \)[/tex]
